hw many types of identity matrix are there

The identity matrix (often denoted with a capital I) of a particular size is unique. In other words, there is only one 2x2 identity matrix (often denoted I sub 2.) However there is a different identity matrix for every size where the number of rows and columns are equal (called square matrices.) However you can still (almost) think of the identity matrix as unique because these different size matrices don't interact with each other. For instance, you can't multiply a 2x2 matrix with I sub 3.